LOT of speculation and conjecture about that.
The church in Ethiopia claims to have the Ark, they keep it in a chapel where a guardian spends his entire life keeping watch over... something (the Ark or not). Before he dies he picks another man to be guardian.
It used to be that the Ark was brought out during festivals. Always covered, so that it could not be seen. There is a photograph from Fifties/Sixties that shows a black-covered object, about the size of a trunk, being hoisted aloft during a festival. Depending on who you believe, it's the only photograph known to exist of the Ark of the Covenant.
LOT of speculation and conjecture about that.
But what does God say on the matter?
(ESV) And when you have multiplied and been fruitful in the land, in those days, declares the LORD, they shall no more say, “The ark of the covenant of the LORD.” It shall not come to mind or be remembered or missed; it shall not be made again.
There was something new to focus on. The New Covenant.
But it didn’t go away. God tells us where it is.